The results obtained in the previous section are based on several strong assumptions, in particular that the excitation temperature of \(^{12}\mathrm {CO}\)  and \(^{13}\mathrm {CO}\)  are equal. To adress this issue, we investigated the application of a second method that does not require this assumption to determine the mass of the gas towards our field of observations using CO lines. We used the LVG model for an expanding spherical shell (e.g. [1]}, [2]}) to model the lines observed. This model require a local, large velocity gradient \(\nabla v\)  along the line of sight. We consider that this assumption is verified throughout the field of observation as the linewidth of \(^{12}\) CO lines suggest typical turbulent broadening (Sect. REF ). We used the non-LTE radiative transfer RADEX code [3]}, a computer program solving the radiative transfer equation based on the escape probability formulation in an isothermal and homogeneous medium characterized by a large velocity gradient. Three geometries are available, we selected the expanding spherical shell for which the escape probability is related to the optical depth \(\tau \)  by the following formula [4]}:
\(\beta _\mathrm {LVG}=\frac{1-e^{-\tau }}{\tau }.\) 
